Whether the intention of receiving the sacrament of Baptism is required on the part of the one baptized?

Objections

Objection 1 : It seems that the intention of receiving the sacrament of Baptism is not required on the part of the one baptized. For the one baptized is, as it were, "patient" in the sacrament. But an intention is required not on the part of the patient but on the part of the agent. Therefore it seems that the intention of receiving Baptism is not required on the part of the one baptized.
Objection 2 : Further, if what is necessary for Baptism be omitted, the Baptism must be repeated; for instance, if the invocation of the Trinity be omitted, as stated above (Question [66], Article [9], ad 3). But it does not seem that a man should be rebaptized through not having had the intention of receiving Baptism: else, since his intention cannot be proved, anyone might ask to be baptized again on account of his lack of intention. Therefore it seems that no intention is required on the part of the one baptized, in order that he receive the sacrament.
Objection 3 : Further, Baptism is given as a remedy for original sin. But original sin is contracted without the intention of the person born. Therefore, seemingly, Baptism requires no intention on the part of the person baptized.